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NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM

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Abstract

We study criteria for deciding when the normal subgroup generated by a single special polynomial automorphism of 𝔸n is as large as possible, namely, equal to the normal closure of the special linear group in the special automorphism group. In particular, we investigate m-triangular automorphisms, i.e., those that can be expressed as a product of affine automorphisms and m triangular automorphisms. Over a field of characteristic zero, we show that every nontrivial 4-triangular special automorphism generates the entire normal closure of the special linear group in the special tame subgroup, for any dimension n ≥ 2. This generalizes a result of Furter and Lamy in dimension 2.

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  1. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, 36688, USA

    D. LEWIS

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  1. D. LEWIS
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LEWIS, D. NORMAL SUBGROUPS GENERATED BY A SINGLE POLYNOMIAL AUTOMORPHISM. Transformation Groups 25, 177–189 (2020). https://doi.org/10.1007/s00031-019-9511-3

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